The mechanics of SGLD [1]} are similar to those of SGD. However, in SGLD, a Guassian noise is injected into Eq. REF  that depends on the step size \(\eta _t \sim N(0,\eta _t\mathbf {I})\) . The Gaussian noise prevents parameter updates to collapse to just the MAP solution, but allows convergence to samples from the true posterior distribution. This approach makes SGLD efficient with large datasets while providing a much-needed Bayesian interpretation to parameter uncertainty. Specifically, for our real-time estimation scheme at each iteration \(t\) , a mini-batch \(\lbrace D^{(\tilde{t},i)}\rbrace _{i=1,2,\cdots ,N_{\tilde{t}}}\)  of size \(N_{\tilde{t}}\)  is used to update the SGLD parameters according to:
\(&\nabla (K^t_L,T^t_L) = \frac{\eta _t}{2}\Bigg ( \nabla \log P(K_L^t,T_L^t) +\frac{N_{\tilde{t}}{n}}{\sum }_{i=1}^{n}\nabla \log P(\dot{a}_i | a_i, u_i, K_L^t, T_L^t)\Bigg )+ \epsilon _t \\&\epsilon _t \sim \mathcal {N}(0,\eta _t\mathbf {I})\) 
